The determination of the orientation of an object's axes relative to a reference system is often of interest. Depending on the application, the orientation and reference system may be in two dimensions (2D) or in three dimensions (3D). In the case of two-dimensional systems, terms such as azimuth, heading, elevation, pitch, and inclination may be used in place of attitude.
There are many techniques in use to measure 2D and 3D attitude. Common techniques include using a magnetic compass to reference the object of interest to the local gravitational field, optical techniques to reference the object of interest to an earth-based or star-based reference frame, accelerometers to measure relative attitude or changes in attitude, and optical and mechanical gyroscopes for also measuring relative attitude. The merits of each technique are best judged according to the specific application or use. Likewise, each technique also exhibits disadvantages that may include accuracy, cost, and ease of use.
Recently, attitude determination using highly accurate space-based radio navigation systems has become possible. Such a radio navigation system is commonly referred to as a Global Navigation Satellite System (GNSS). A GNSS includes a network of satellites that broadcast radio signals, enabling a user to determine the location of a receiving antenna with a high degree of accuracy. To determine the attitude of an object, it is simply necessary to determine the position of two or more receiving antennas that have known placements relative to an object. Examples of GNSS systems include Navstar Global Positioning System (GPS), established by the United States; Globalnaya Navigatsionnay Sputnikovaya Sistema, or Global Orbiting Navigation Satellite System (GLONASS), established by the Russian Federation and similar in concept to GPS; and Galileo, also similar to GPS but created by the European Community and slated for full operational capacity in 2008.
Should it be necessary to improve the accuracy, reliability, or confidence level of an attitude or position determined through use of a GNSS, a Satellite-Based Augmentation System (SBAS) may be incorporated if one that is suitable is available. There are several public SBAS that work with GPS. These include Wide Area Augmentation System (WAAS), developed by the United States' Federal Aviation Authority, European Geostationary Navigation Overlay Service (EGNOS), developed by the European Community, as well as other public and private pay-for-service systems.
Currently the best-known of the available GNSS, GPS was developed by the United States government and has a constellation of 24 satellites in 6 orbital planes at an altitude of approximately 26,500 km. The first satellite was launched in February 1978. Initial Operational Capability (IOC) for the GPS was declared in December 1993. Each satellite continuously transmits microwave L-band radio signals in two frequency bands, L1 (1575.42 MHz) and L2 (1227.6 MHz). The L1 and L2 signals are phase shifted, or modulated, by one or more binary codes. These binary codes provide timing patterns relative to the satellite's onboard precision clock (synchronized to other satellites and to a ground reference through a ground-based control segment), in addition to a navigation message giving the precise orbital position of each satellite, clock correction information, and other system parameters.
The binary codes providing the timing information are called the C/A Code, or coarse acquisition code, and the P-code, or precise code. The C/A Code is a 1 MHz Pseudo Random Noise (PRN) code modulating the phase of the L1 signal, and repeating every 1023 bits (one millisecond). The P-Code is also a PRN code, but modulates the phase of both the L1 and L2 signals, and is a 10 MHz code repeating every seven days. These PRN codes are known patterns that can be compared to internal versions in the receiver. The GNSS receiver is able to compute an unambiguous range to each satellite by determining the time-shift necessary to align the internal code to the broadcast code. Since both the C/A Code and the P-Code have a relatively long “wavelength”—approximately 300 meters (or 1 microsecond) for the C/A Code, and 30 meters (or 1/10 microsecond) for the P-Code, positions computed using them have a relatively coarse level of resolution.
To improve the positional accuracy provided by use of the C/A Code and the P-Code, a receiver may take advantage of the carrier component of the L1 or L2 signal. The term “carrier”, as used herein, refers to the dominant spectral component remaining in the radio signal after the spectral content resulting from the modulating PRN digital codes has been removed (e.g., from the C/A Code and the P-Code). The L1 and L2 carrier signals have wavelengths of about 19 centimeters and 24 centimeters, respectively. The GPS receiver is able to track these carrier signals and measure the carrier phase to a small fraction of a complete wavelength, permitting range measurement to an accuracy of less than a centimeter.
A final technique to improve accuracy, and which shall be seen to be of key interest here, is the technique of differencing GPS range measurements—known as Differential GPS (DGPS). The combination of DGPS with precise measurements of carrier phase leads to differential position accuracies of less than one centimeter root-mean-squared (i.e., centimeter-level positioning). Such accuracies are sufficient to determine the attitude of an object with 2 or more GPS GNSS antennas, typically spaced from 0.2 meters to 2 meters apart.
Therefore, what is needed in the art is a system that utilizes Global Navigation Satellite System (GNSS) signals to infer differential path length of carrier signals arriving at two or more antennas to ultimately determine attitude while leveraging the advantages of geometry constraints of the antennas attached to a rigid body, and does so with measurements from all antennas processed simultaneously and optimally.